Why can't I use Loop Cut on certain parts of my mesh?
You can only loop cut through quadrilateral faces in a line, like a row of rectangles. A loop cut through a triangle would divide one of the vertices, but that can't happen. N-gons also don't work well with it. See Anthony Forwood's comment:


  Quads are ideal, tris when necessary, and ngons only when absolutely necessary.


It has nothing to do with the F function.